# Research on Automatic Parking System Strategy

^{*}

## Abstract

**:**

## 1. Introduction

## 2. The Initialization Program

#### 2.1. Vehicle Kinematics Model

#### 2.2. Kinematic Constraints

#### 2.3. Boundary Conditions

#### 2.4. Weighted Ring Graph

## 3. Parking Path Planning

#### 3.1. Bidirectional Breadth-First Search Design Based on Parking Environment

#### 3.2. Traditional Bellman–Ford Algorithm

#### 3.3. Modified Bellman–Ford Algorithm

#### 3.4. Parking Paths Smooth

- (1)
- The zero-th boundary condition. The condition satisfies the relation: ${c}_{n}=0,{c}_{1}=0$.
- (2)
- The first boundary condition. At the endpoint, the first derivative is given, and if ${S}_{1}^{\prime}\left({x}_{1}\right)={p}_{1}$ and ${S}_{step-1}^{\prime}\left({x}_{step}\right)={p}_{step}$, the following relationship is satisfied.$$\left\{\begin{array}{c}2{\delta}_{1}{c}_{1}+{\delta}_{1}{c}_{2}=3\left({\u2206}_{1}/{\delta}_{1}-{p}_{1}\right)\\ {\delta}_{step-1}{c}_{step-1}+2{\delta}_{step-1}{c}_{step-1}=3\left({p}_{step}-{\u2206}_{step-1}/{\delta}_{step-1}\right)\end{array}\right.$$
- (3)
- The second boundary condition. For the second derivative of a given endpoint, if ${S}_{1}^{\u2033}\left({x}_{1}\right)={p}_{1}$ and ${S}_{step-1}^{\u2033}\left({x}_{step}\right)={p}_{step}$, the following relation can be deduced.$$\left\{\begin{array}{c}2{c}_{1}={p}_{1}\\ 2{c}_{step}={p}_{step}\end{array}\right.$$

## 4. Results and Discussion

#### 4.1. Comparison of Experimental Results between Proposed Automatic Parking System and Traditional Path Planning Strategy

#### 4.2. Comparison of Experimental Results between Proposed Automatic Parking System and Similar Path Planning Strategy

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Vehicle and parking space diagram. $A,B,C$ and $D$ are the four boundary points of the car respectively.

**Figure 3.**Grid map sketches. $A,B,C$ and $D$ are the four boundary points of the car respectively. $E$ and $F$ are the grids in the middle of the car.

**Figure 4.**Schematic diagram of ring graph ring diagram $Dis$ based on grid map. (

**a**) Normal; (

**b**) obstructions; (

**c**) garages; (

**d**) garages and obstructions.

**Figure 5.**Schematic diagram of bidirectional breadth-first search algorithm. $S$ is the source point, $N$ is the end point, $\mathrm{k}1,\mathrm{k}2$ and $\mathrm{k}3$ are different search layers.

**Figure 7.**The grid map moving path formed based on the algorithm in this paper. (

**a**) Ideal condition; (

**b**) traffic ahead; (

**c**) few obstacles beside the parking space; (

**d**) many obstacles beside the parking space.

**Figure 8.**Comparison diagram of successful parking effects of the two strategies in different parking environments under actual and ideal conditions. (

**a**) Comparison diagram of successful parking effect in different environments under ideal conditions; (

**b**) comparison diagram of successful parking effect in different environments under actual conditions. ICE: ideal conditions (excellent); GCE: general complex conditions (excellent); ECCE: extremely complex conditions (excellent); ICG: ideal conditions (good); GCG: general complex conditions (good); ECCG: extremely complex conditions (good); ICM: ideal conditions (medium); GCM: general complex conditions (medium); ECCM: extremely complex conditions (medium); ICA: ideal conditions (average); GCA: general complex conditions (average); ECCA: extremely complex conditions (average).

Item | Parameter | |
---|---|---|

Experimental vehicle parameters | Width/W_{d} | 17.8 cm |

Wheel base/h_{m} | 19.4 cm | |

Length/L | 28.5 cm | |

Distance between front wheel axle and nose/L_{begin} | 5.4 cm | |

Distance between rear axle and rear axle/L_{end} | 2.5 cm | |

Minimum turning radius/R_{min} | 33.28 cm | |

Experimental site parameters | Length/Cow | 118.9 cm |

Width/Col | 84.1 cm | |

Number of parking Spaces available | 1 | |

Boundary condition | One side of the parking space is shielded with a height of about 40 cm |

**Table 2.**Comparison of Experimental Results between Proposed Automatic Parking System and Traditional Path Planning Strategy.

Traditional | Proposed | |||||||
---|---|---|---|---|---|---|---|---|

Experiment Conditions | Actual Success Rate | Ideal Success Rate | Average Vehicle Moving Time (s) | Average Algorithm Running Time (ms) | Actual Success Rate | Ideal Success Rate | Average Vehicle Moving Time (s) | Average Algorithm Running Time (ms) |

Ideal conditions | 86.7% | 90.0% | 47.3743 | 1.010 | 84.3% | 100% | 47.2273 | 7297.2 |

General complex conditions | 60.0% | 73.3% | 44.7203 | 1.003 | 63.3% | 90.0% | 45.0593 | 7870.1 |

Extremely complex conditions | 0.0% | 53.3% | 47.9330 | 1.001 | 23.3% | 66.7% | 50.2448 | 10,599.4 |

n, m | The Similar Method | The Proposed Strategy | ||
---|---|---|---|---|

Step Number | Computing Time (ms) | Step Number | Computing Time (ms) | |

$n=80,m=40$ | 82 | 3.75 | 78 | 732.11 |

$n=85,m=45$ | 86 | 4.09 | 86 | 783.56 |

$n=90,m=40$ | 91 | 5.21 | 89 | 964.29 |

$n=90,m=45$ | 91 | 5.87 | 90 | 981.01 |

$n=95,m=50$ | 94 | 6.88 | 89 | 1035.22 |

$n=100,m=50$ | 99 | 7.55 | 92 | 1104.21 |

$n=105,m=55$ | 108 | 7.92 | 101 | 1326.89 |

$n=110,m=55$ | 113 | 9.69 | 104 | 1568.53 |

$n=120,m=60$ | 121 | 10.63 | 115 | 1925.16 |

$n=125,m=65$ | 130 | 12.01 | 120 | 2011.05 |

n, m | The Similar Method | The Proposed Strategy | ||
---|---|---|---|---|

Step Number | Computing Time (ms) | Step Number | Computing Time (ms) | |

$n=80,m=40$ | 96 | 5.23 | 91 | 812.25 |

$n=85,m=45$ | 105 | 7.86 | 100 | 901.02 |

$n=90,m=40$ | 121 | 8.05 | 119 | 1021.01 |

$n=90,m=45$ | 133 | 9.42 | 121 | 1125.69 |

$n=95,m=50$ | 145 | 10.21 | 136 | 1368.53 |

$n=100,m=50$ | 151 | 11.85 | 141 | 1685.57 |

$n=105,m=55$ | 167 | 12.05 | 157 | 1956.58 |

$n=110,m=55$ | 187 | 15.36 | 174 | 2012.55 |

$n=120,m=60$ | 192 | 17.69 | 182 | 2114.09 |

$n=125,m=65$ | 201 | 19.62 | 191 | 2456.38 |

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**MDPI and ACS Style**

Zhang, C.; Zhou, R.; Lei, L.; Yang, X.
Research on Automatic Parking System Strategy. *World Electr. Veh. J.* **2021**, *12*, 200.
https://doi.org/10.3390/wevj12040200

**AMA Style**

Zhang C, Zhou R, Lei L, Yang X.
Research on Automatic Parking System Strategy. *World Electric Vehicle Journal*. 2021; 12(4):200.
https://doi.org/10.3390/wevj12040200

**Chicago/Turabian Style**

Zhang, Chuanwei, Rui Zhou, Lei Lei, and Xinyue Yang.
2021. "Research on Automatic Parking System Strategy" *World Electric Vehicle Journal* 12, no. 4: 200.
https://doi.org/10.3390/wevj12040200